From Guild Wars Wiki
miniatures receive when added in the Hall of Monuments. It is similar to customization in that it can be done only once and is player specific, but instead of completely preventing use by other players, it merely prevents that miniature from being displayed in other players' Halls.Dedication is a permanent status that
- Before the 12 October 2007 game update, the Hall of Monuments allowed players to customize miniatures instead. If you take a customized miniature back to the Hall of Monuments, it will give you the option to remove the customization and dedicate the miniature instead.
- These customized miniatures display in the HoM Calculator without adverse effects.
- Dedicating a miniature at a "Devotion" monument ties it to that particular character, and no other character on your account.